The equilibration of an axisymmetric, linearly poroelastic layer of finite thickness is determined given an immobile, impermeable base and an impermeable, stress-free top surface. Analytical and numerical studies show that there are eigenfunctions corresponding to sites of fluid injection and removal. Numerical studies also show that an increase in effective stiffness accelerates the equilibration of initial disturbances with longer wavelengths. A Gaussian initial displacement is shown to spread radially rather than simply decaying in amplitude.

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